And, by running free in Jamaica on Wednesday afternoon, the heifer might have earned herself a reprieve from the slaughterhouse from which she escaped, officials said.

Police officers first confronted the 350-pound heifer about 2 p.m. and called in the Emergency Service Unit for help in pursuing her through about a mile of city streets. The officers finally corralled the calf in a fenced-off space between two houses, and by 3:30 p.m. had delivered her to a shelter in Brooklyn operated by Animal Care and Control of New York City.

There she got a name.

“We named her Molly,” said Richard P. Gentles, a spokesman for the city agency.

The police said the slaughterhouse from which the heifer came was in the area of 158th Street and Beaver Road. There are several slaughterhouses in that area, but none came forward immediately to claim the heifer, Mr. Gentles said.

“We want her to live,” he said. “We want her to live out her life, absolutely.”

Mr. Gentles said the agency had already contacted Farm Sanctuary, a vegan farm in the Finger Lakes region of upstate New York that takes in animals found running loose in New York City, and called other sanctuaries as well.

He said Molly arrived at the shelter in good condition.

“She was erect and walking when she came in,” he said.

Black, with a yellow tag with a number affixed to her back, Mr. Gentles said the heifer was being fed and evaluated by the shelter’s medical department. “We got it set up so she has hay and water and all that good stuff,” he said.

Earlier, her fate was less clear.

After decamping from the slaughterhouse, the heifer made a mad dash along 94th Avenue, turned at 150th Street, and again at Liberty Avenue, witnesses said. She passed other slaughterhouses  for goats, lambs, chickens and turkeys.

“It was running, it was running, it was running,” said Dwain Abrams, 23, a dollar van driver who watched as officers and others trailed. “It was crazy.”

When the heifer got to the area of 109th Avenue and Sutphin Boulevard, she drew the attention of Bill Barksdale, 73, who was taking advantage of a few hours of clear skies to plant in his garden. He heard people screaming, looked over and saw the heifer trotting with police cars slowly trailing  their lights and sirens noticeably turned off.

“The sun comes out and the cows come out, too,” he said.

The heifer went through a wide gate into the front yard of a house adjacent to Mr. Barksdale’s. She went to the back of the house, crossed a weedy patch, climbed over some broken cement pieces and got trapped in the space between the fence of one house and the stone wall of another.

Officers eventually lassoed the animal with a rope, witnesses said. The police said a tranquilizer dart was fired at the heifer to subdue her.

Adam Khan, 47, a truck driver who lives in a house near where the calf was captured, said the episode “tells you something.”